(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 10.4' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[    139234,       4012]
NotebookOptionsPosition[    127739,       3645]
NotebookOutlinePosition[    131541,       3751]
CellTagsIndexPosition[    131386,       3744]
WindowTitle->DiracTrace
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[GridBox[{
   {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{
     Cell[BoxData[
      ActionMenuBox[
       FrameBox[
        InterpretationBox[Cell[TextData[{
          "See Also",
          StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow",
           StripOnInput->False]
         }]],
         TextCell[
          Row[{"See Also", 
            Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]],
        StripOnInput->False], {"\<\"Contract\"\>":>Documentation`HelpLookup[
       "paclet:FeynCalc/ref/Contract"], "\<\"DiracEquation\"\>":>
       Documentation`HelpLookup[
       "paclet:FeynCalc/ref/DiracEquation"], "\<\"DiracGamma\"\>":>
       Documentation`HelpLookup[
       "paclet:FeynCalc/ref/DiracGamma"], "\<\"DiracGammaExpand\"\>":>
       Documentation`HelpLookup[
       "paclet:FeynCalc/ref/DiracGammaCombine"], "\<\"DiracTrick\"\>":>
       Documentation`HelpLookup[
       "paclet:FeynCalc/ref/DiracTrick"], "\<\"FCGetDiracGammaScheme\"\>":>
       Documentation`HelpLookup[
       "paclet:FeynCalc/ref/FCSetDiracGammaScheme"], \
"\<\"FCSetDiracGammaScheme\"\>":>Documentation`HelpLookup[
       "paclet:FeynCalc/ref/FCGetDiracGammaScheme"]},
       Appearance->None,
       MenuAppearance->Automatic,
       MenuStyle->"SeeAlso"]],
      LineSpacing->{1.4, 0}],
     "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\
\[ThickSpace]",
     Cell[BoxData[
      ActionMenuBox[
       FrameBox[
        InterpretationBox[Cell[TextData[{
          "URL",
          StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow",
           StripOnInput->False]
         }]],
         TextCell[
          Row[{"URL", 
            Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]],
        StripOnInput->False], {"\<\"FeynCalc/ref/DiracTrace\"\>":>
       None, "\<\"Copy Wolfram Documentation Center URL\"\>":>
       Module[{DocumentationSearch`Private`nb$}, 
        DocumentationSearch`Private`nb$ = NotebookPut[
           Notebook[{
             Cell["FeynCalc/ref/DiracTrace"]}, Visible -> False]]; 
        SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; 
        FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; 
        NotebookClose[DocumentationSearch`Private`nb$]; Null], 
       Delimiter, "\<\"Copy web URL\"\>":>
       Module[{DocumentationSearch`Private`nb$}, 
        DocumentationSearch`Private`nb$ = NotebookPut[
           Notebook[{
             Cell[
              BoxData[
               MakeBoxes[
                Hyperlink[
                "http://reference.wolfram.com/language/FeynCalc/ref/\
DiracTrace.html"], StandardForm]], "Input", TextClipboardType -> 
              "PlainText"]}, Visible -> False]]; 
        SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; 
        FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; 
        NotebookClose[DocumentationSearch`Private`nb$]; 
        Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{
         NotebookLocate[{
           URL[
            StringJoin[
             If[
              TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$72204], 
              "http://reference.wolfram.com/system-modeler/", 
              "http://reference.wolfram.com/language/"], 
             "FeynCalc/ref/DiracTrace", ".html"]], None}]}]},
       Appearance->None,
       MenuAppearance->Automatic,
       MenuStyle->"URLMenu"]],
      LineSpacing->{1.4, 0}]
    }], "AnchorBar"]}
  }]], "AnchorBarGrid",
 GridBoxOptions->{GridBoxItemSize->{"Columns" -> {
     Scaled[0.65], {
      Scaled[0.34]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, 
   "RowsIndexed" -> {}}},
 CellID->1],

Cell[TextData[{
 Cell["DiracTrace", "ObjectName"],
 Cell[BoxData[
  InterpretationBox[
   StyleBox[
    GraphicsBox[{},
     BaselinePosition->Baseline,
     ImageSize->{8, 0}],
    CacheGraphics->False],
   Spacer[8]]]],
 Cell[BoxData[""], "ObjectNameTranslation"]
}], "ObjectNameGrid"],

Cell[CellGroupData[{

Cell[BoxData[GridBox[{
   {"", Cell[TextData[{
     Cell[BoxData[
      RowBox[{"DiracTrace", "[", "exp", "]"}]], "InlineFormula"],
     " \[LineSeparator]is the head of Dirac traces. By default the trace is \
not evaluated. The evaluation occurs only when the option ",
     ButtonBox["DiracTraceEvaluate",
      BaseStyle->"Link",
      ButtonData->"paclet:FeynCalc/ref/DiracTraceEvaluate",
      ButtonNote->"DiracTraceEvaluate"],
     " is set to ",
     Cell[BoxData["True"], "InlineFormula"],
     ". It is recommended to use ",
     ButtonBox["DiracSimplify",
      BaseStyle->"Link",
      ButtonData->"paclet:FeynCalc/ref/DiracSimplify",
      ButtonNote->"DiracSimplify"],
     ", which will automatically evaluate all Dirac traces in the input \
expression."
    }]]}
  }]], "Usage",
 GridBoxOptions->{
 GridBoxBackground->{
  "Columns" -> {{None}}, "ColumnsIndexed" -> {}, "Rows" -> {{None}}, 
   "RowsIndexed" -> {}}},
 CellID->982511436],

Cell[CellGroupData[{

Cell[TextData[Cell[BoxData[
 ButtonBox[Cell[TextData[{
   Cell[BoxData[
    InterpretationBox[
     StyleBox[
      GraphicsBox[{},
       BaselinePosition->Baseline,
       ImageSize->{6, 0}],
      CacheGraphics->False],
     Spacer[6]]]],
   "Details"
  }], "NotesFrameText"],
  Appearance->{Automatic, None},
  BaseStyle->None,
  ButtonFunction:>(FrontEndExecute[{
     FrontEnd`SelectionMove[
      FrontEnd`SelectedNotebook[], All, ButtonCell], 
     FrontEndToken["OpenCloseGroup"], 
     FrontEnd`SelectionMove[
      FrontEnd`SelectedNotebook[], After, CellContents]}]& ),
  Evaluator->None,
  Method->"Preemptive"]]]], "NotesSection",
 WholeCellGroupOpener->True,
 CellGroupingRules->{"SectionGrouping", 50},
 CellID->894721589],

Cell["", "SectionHeaderSpacer"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Options", "[", "DiracTrace", "]"}]], "Input",
 CellLabel->"In[72]:="],

Cell[BoxData[
 FormBox[
  RowBox[{"{", 
   RowBox[{
    RowBox[{"Contract", "\[Rule]", "True"}], ",", 
    RowBox[{"DiracTraceEvaluate", "\[Rule]", "False"}], ",", 
    RowBox[{"EpsContract", "\[Rule]", "False"}], ",", 
    RowBox[{"Expand", "\[Rule]", "True"}], ",", 
    RowBox[{"FCVerbose", "\[Rule]", "False"}], ",", 
    RowBox[{"Factoring", "\[Rule]", "Automatic"}], ",", 
    RowBox[{"FeynCalcExternal", "\[Rule]", "False"}], ",", 
    RowBox[{"FeynCalcInternal", "\[Rule]", "False"}], ",", 
    RowBox[{"Mandelstam", "\[Rule]", 
     RowBox[{"{", "}"}]}], ",", 
    RowBox[{"PairCollect", "\[Rule]", "False"}], ",", 
    RowBox[{"Sort", "\[Rule]", "True"}], ",", 
    RowBox[{"Schouten", "\[Rule]", "0"}], ",", 
    RowBox[{"TraceOfOne", "\[Rule]", "4"}], ",", 
    RowBox[{"West", "\[Rule]", "True"}]}], "}"}], TraditionalForm]], "Output",\

 ImageSize->{493, 73},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[72]="]
}, Open  ]]
}, Closed]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 Cell[BoxData[
  InterpretationBox[
   StyleBox[
    GraphicsBox[{},
     BaselinePosition->Baseline,
     ImageSize->{6, 0}],
    CacheGraphics->False],
   Spacer[6]]]],
 "Examples",
 "\[NonBreakingSpace]\[NonBreakingSpace]",
 Cell["(10)", "ExampleCount"]
}], "PrimaryExamplesSection",
 WholeCellGroupOpener->True,
 CellTags->"PrimaryExamplesSection",
 CellID->1070442148],

Cell[CellGroupData[{

Cell[TextData[{
 "Basic Examples",
 "\[NonBreakingSpace]\[NonBreakingSpace]",
 Cell["(10)", "ExampleCount"]
}], "ExampleSection", "ExampleSection",
 WholeCellGroupOpener->True,
 CellID->1068112497],

Cell["There is no automatic evaluation of Dirac traces", "Notes"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DiracTrace", "[", 
  RowBox[{"GA", "[", 
   RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}], "]"}]], "Input",
 CellTags->"DiracTrace",
 CellLabel->"In[1]:=",
 CellID->60676203],

Cell[BoxData[
 FormBox[
  RowBox[{"tr", "(", 
   FormBox[
    RowBox[{
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox[
        FormBox["\[Mu]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox[
        FormBox["\[Nu]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm]}],
    TraditionalForm], ")"}], TraditionalForm]], "Output",
 ImageSize->{72, 19},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"DiracTrace",
 CellLabel->"Out[1]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DiracTrace", "[", 
  RowBox[{"GA", "[", 
   RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Sigma]"}], "]"}], 
  "]"}]], "Input",
 CellTags->"DiracTrace",
 CellLabel->"In[2]:=",
 CellID->1088537337],

Cell[BoxData[
 FormBox[
  RowBox[{"tr", "(", 
   FormBox[
    RowBox[{
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox[
        FormBox["\[Mu]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox[
        FormBox["\[Nu]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox[
        FormBox["\[Rho]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox[
        FormBox["\[Sigma]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm]}],
    TraditionalForm], ")"}], TraditionalForm]], "Output",
 ImageSize->{123, 19},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"DiracTrace",
 CellLabel->"Out[2]="]
}, Open  ]],

Cell[TextData[{
 "You can either set the option ",
 ButtonBox["DiracTraceEvaluate",
  BaseStyle->"Link",
  ButtonData->"paclet:FeynCalc/ref/DiracTraceEvaluate",
  ButtonNote->"DiracTraceEvaluate"],
 " to ",
 Cell[BoxData["True"], "InlineFormula"],
 " or use ",
 ButtonBox["DiracSimplify",
  BaseStyle->"Link",
  ButtonData->"paclet:FeynCalc/ref/DiracSimplify",
  ButtonNote->"DiracSimplify"],
 "."
}], "Notes"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DiracTrace", "[", 
  RowBox[{
   RowBox[{"GA", "[", 
    RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Sigma]"}], "]"}], 
   ",", 
   RowBox[{"DiracTraceEvaluate", "\[Rule]", "True"}]}], "]"}]], "Input",
 CellTags->"DiracTrace",
 CellLabel->"In[3]:=",
 CellID->710007181],

Cell[BoxData[
 FormBox[
  RowBox[{"4", " ", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{
      SuperscriptBox[
       OverscriptBox["g", "_"], 
       RowBox[{
        FormBox[
         FormBox["\[Mu]",
          TraditionalForm],
         TraditionalForm], 
        FormBox[
         FormBox["\[Sigma]",
          TraditionalForm],
         TraditionalForm]}]], " ", 
      SuperscriptBox[
       OverscriptBox["g", "_"], 
       RowBox[{
        FormBox[
         FormBox["\[Nu]",
          TraditionalForm],
         TraditionalForm], 
        FormBox[
         FormBox["\[Rho]",
          TraditionalForm],
         TraditionalForm]}]]}], "-", 
     RowBox[{
      SuperscriptBox[
       OverscriptBox["g", "_"], 
       RowBox[{
        FormBox[
         FormBox["\[Mu]",
          TraditionalForm],
         TraditionalForm], 
        FormBox[
         FormBox["\[Rho]",
          TraditionalForm],
         TraditionalForm]}]], " ", 
      SuperscriptBox[
       OverscriptBox["g", "_"], 
       RowBox[{
        FormBox[
         FormBox["\[Nu]",
          TraditionalForm],
         TraditionalForm], 
        FormBox[
         FormBox["\[Sigma]",
          TraditionalForm],
         TraditionalForm]}]]}], "+", 
     RowBox[{
      SuperscriptBox[
       OverscriptBox["g", "_"], 
       RowBox[{
        FormBox[
         FormBox["\[Mu]",
          TraditionalForm],
         TraditionalForm], 
        FormBox[
         FormBox["\[Nu]",
          TraditionalForm],
         TraditionalForm]}]], " ", 
      SuperscriptBox[
       OverscriptBox["g", "_"], 
       RowBox[{
        FormBox[
         FormBox["\[Rho]",
          TraditionalForm],
         TraditionalForm], 
        FormBox[
         FormBox["\[Sigma]",
          TraditionalForm],
         TraditionalForm]}]]}]}], ")"}]}], TraditionalForm]], "Output",
 ImageSize->{270, 19},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"DiracTrace",
 CellLabel->"Out[3]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DiracSimplify", "[", 
  RowBox[{"DiracTrace", "[", 
   RowBox[{"GA", "[", 
    RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Sigma]"}], "]"}], 
   "]"}], "]"}]], "Input",
 CellLabel->"In[4]:="],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"4", " ", 
    SuperscriptBox[
     OverscriptBox["g", "_"], 
     RowBox[{
      FormBox[
       FormBox["\[Mu]",
        TraditionalForm],
       TraditionalForm], 
      FormBox[
       FormBox["\[Sigma]",
        TraditionalForm],
       TraditionalForm]}]], " ", 
    SuperscriptBox[
     OverscriptBox["g", "_"], 
     RowBox[{
      FormBox[
       FormBox["\[Nu]",
        TraditionalForm],
       TraditionalForm], 
      FormBox[
       FormBox["\[Rho]",
        TraditionalForm],
       TraditionalForm]}]]}], "-", 
   RowBox[{"4", " ", 
    SuperscriptBox[
     OverscriptBox["g", "_"], 
     RowBox[{
      FormBox[
       FormBox["\[Mu]",
        TraditionalForm],
       TraditionalForm], 
      FormBox[
       FormBox["\[Rho]",
        TraditionalForm],
       TraditionalForm]}]], " ", 
    SuperscriptBox[
     OverscriptBox["g", "_"], 
     RowBox[{
      FormBox[
       FormBox["\[Nu]",
        TraditionalForm],
       TraditionalForm], 
      FormBox[
       FormBox["\[Sigma]",
        TraditionalForm],
       TraditionalForm]}]]}], "+", 
   RowBox[{"4", " ", 
    SuperscriptBox[
     OverscriptBox["g", "_"], 
     RowBox[{
      FormBox[
       FormBox["\[Mu]",
        TraditionalForm],
       TraditionalForm], 
      FormBox[
       FormBox["\[Nu]",
        TraditionalForm],
       TraditionalForm]}]], " ", 
    SuperscriptBox[
     OverscriptBox["g", "_"], 
     RowBox[{
      FormBox[
       FormBox["\[Rho]",
        TraditionalForm],
       TraditionalForm], 
      FormBox[
       FormBox["\[Sigma]",
        TraditionalForm],
       TraditionalForm]}]]}]}], TraditionalForm]], "Output",
 ImageSize->{282, 16},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[4]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DiracTrace", "[", 
  RowBox[{"GS", "[", 
   RowBox[{"p", ",", "q", ",", "r", ",", "s"}], "]"}], "]"}]], "Input",
 CellLabel->"In[5]:="],

Cell[BoxData[
 FormBox[
  RowBox[{"tr", "(", 
   FormBox[
    RowBox[{
     RowBox[{"(", 
      FormBox[
       RowBox[{
        OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", 
        FormBox[
         OverscriptBox[
          FormBox["p",
           TraditionalForm], "_"],
         TraditionalForm]}],
       TraditionalForm], ")"}], ".", 
     RowBox[{"(", 
      FormBox[
       RowBox[{
        OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", 
        FormBox[
         OverscriptBox[
          FormBox["q",
           TraditionalForm], "_"],
         TraditionalForm]}],
       TraditionalForm], ")"}], ".", 
     RowBox[{"(", 
      FormBox[
       RowBox[{
        OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", 
        FormBox[
         OverscriptBox[
          FormBox["r",
           TraditionalForm], "_"],
         TraditionalForm]}],
       TraditionalForm], ")"}], ".", 
     RowBox[{"(", 
      FormBox[
       RowBox[{
        OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", 
        FormBox[
         OverscriptBox[
          FormBox["s",
           TraditionalForm], "_"],
         TraditionalForm]}],
       TraditionalForm], ")"}]}],
    TraditionalForm], ")"}], TraditionalForm]], "Output",
 ImageSize->{220, 16},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[5]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DiracSimplify", "[", "%", "]"}]], "Input",
 CellLabel->"In[6]:="],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"4", " ", 
    RowBox[{"(", 
     RowBox[{
      FormBox[
       OverscriptBox[
        FormBox["p",
         TraditionalForm], "_"],
       TraditionalForm], 
      FormBox["\<\"\[CenterDot]\"\>",
       TraditionalForm], 
      FormBox[
       OverscriptBox[
        FormBox["s",
         TraditionalForm], "_"],
       TraditionalForm]}], ")"}], " ", 
    RowBox[{"(", 
     RowBox[{
      FormBox[
       OverscriptBox[
        FormBox["q",
         TraditionalForm], "_"],
       TraditionalForm], 
      FormBox["\<\"\[CenterDot]\"\>",
       TraditionalForm], 
      FormBox[
       OverscriptBox[
        FormBox["r",
         TraditionalForm], "_"],
       TraditionalForm]}], ")"}]}], "-", 
   RowBox[{"4", " ", 
    RowBox[{"(", 
     RowBox[{
      FormBox[
       OverscriptBox[
        FormBox["p",
         TraditionalForm], "_"],
       TraditionalForm], 
      FormBox["\<\"\[CenterDot]\"\>",
       TraditionalForm], 
      FormBox[
       OverscriptBox[
        FormBox["r",
         TraditionalForm], "_"],
       TraditionalForm]}], ")"}], " ", 
    RowBox[{"(", 
     RowBox[{
      FormBox[
       OverscriptBox[
        FormBox["q",
         TraditionalForm], "_"],
       TraditionalForm], 
      FormBox["\<\"\[CenterDot]\"\>",
       TraditionalForm], 
      FormBox[
       OverscriptBox[
        FormBox["s",
         TraditionalForm], "_"],
       TraditionalForm]}], ")"}]}], "+", 
   RowBox[{"4", " ", 
    RowBox[{"(", 
     RowBox[{
      FormBox[
       OverscriptBox[
        FormBox["p",
         TraditionalForm], "_"],
       TraditionalForm], 
      FormBox["\<\"\[CenterDot]\"\>",
       TraditionalForm], 
      FormBox[
       OverscriptBox[
        FormBox["q",
         TraditionalForm], "_"],
       TraditionalForm]}], ")"}], " ", 
    RowBox[{"(", 
     RowBox[{
      FormBox[
       OverscriptBox[
        FormBox["r",
         TraditionalForm], "_"],
       TraditionalForm], 
      FormBox["\<\"\[CenterDot]\"\>",
       TraditionalForm], 
      FormBox[
       OverscriptBox[
        FormBox["s",
         TraditionalForm], "_"],
       TraditionalForm]}], ")"}]}]}], TraditionalForm]], "Output",
 ImageSize->{369, 16},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[6]="]
}, Open  ]],

Cell[TextData[{
 "The old methods of evaluating traces by replacing ",
 ButtonBox["DiracTrace",
  BaseStyle->"Link",
  ButtonData->"paclet:FeynCalc/ref/DiracTrace",
  ButtonNote->"DiracTrace"],
 " with ",
 ButtonBox["Tr",
  BaseStyle->"Link",
  ButtonData->"paclet:FeynCalc/ref/Tr",
  ButtonNote->"Tr"],
 " or ",
 ButtonBox["TR",
  BaseStyle->"Link",
  ButtonData->"paclet:FeynCalc/ref/TR",
  ButtonNote->"TR"],
 " are deprecated and should not be used anymore. In particular, they are \
slower are less efficient than using ",
 ButtonBox["DiracSimplify",
  BaseStyle->"Link",
  ButtonData->"paclet:FeynCalc/ref/DiracSimplify",
  ButtonNote->"DiracSimplify"],
 ". "
}], "Notes"],

Cell[CellGroupData[{

Cell[BoxData[
 InterpretationBox[Cell["\t", "ExampleDelimiter"],
  $Line = 0; Null]], "ExampleDelimiter"],

Cell[TextData[{
 "Traces involving ",
 Cell[BoxData[
  SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"],
 " or chirality projectors in ",
 Cell[BoxData["4"], "InlineFormula"],
 "-dimensions are also possible"
}], "Notes"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DiracTrace", "[", 
  RowBox[{"GA", "[", 
   RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Sigma]", ",", "5"}], 
   "]"}], "]"}]], "Input",
 CellTags->"DiracTrace",
 CellLabel->"In[1]:=",
 CellID->196468068],

Cell[BoxData[
 FormBox[
  RowBox[{"tr", "(", 
   FormBox[
    RowBox[{
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox[
        FormBox["\[Mu]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox[
        FormBox["\[Nu]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox[
        FormBox["\[Rho]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox[
        FormBox["\[Sigma]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox["5",
        TraditionalForm]],
      TraditionalForm]}],
    TraditionalForm], ")"}], TraditionalForm]], "Output",
 ImageSize->{147, 22},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"DiracTrace",
 CellLabel->"Out[1]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DiracSimplify", "[", "%", "]"}]], "Input",
 CellLabel->"In[2]:="],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"-", "4"}], " ", "\[ImaginaryI]", " ", 
   SuperscriptBox[
    OverscriptBox["\[Epsilon]", "_"], 
    RowBox[{
     FormBox[
      FormBox["\[Mu]",
       TraditionalForm],
      TraditionalForm], 
     FormBox[
      FormBox["\[Nu]",
       TraditionalForm],
      TraditionalForm], 
     FormBox[
      FormBox["\[Rho]",
       TraditionalForm],
      TraditionalForm], 
     FormBox[
      FormBox["\[Sigma]",
       TraditionalForm],
      TraditionalForm]}]]}], TraditionalForm]], "Output",
 ImageSize->{86, 14},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[2]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DiracTrace", "[", 
  RowBox[{"GA", "[", 
   RowBox[{
   "\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Sigma]", ",", "\[Delta]", 
    ",", "\[Tau]", ",", "5"}], "]"}], "]"}]], "Input",
 CellLabel->"In[3]:="],

Cell[BoxData[
 FormBox[
  RowBox[{"tr", "(", 
   FormBox[
    RowBox[{
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox[
        FormBox["\[Mu]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox[
        FormBox["\[Nu]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox[
        FormBox["\[Rho]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox[
        FormBox["\[Sigma]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox[
        FormBox["\[Delta]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox[
        FormBox["\[Tau]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox["5",
        TraditionalForm]],
      TraditionalForm]}],
    TraditionalForm], ")"}], TraditionalForm]], "Output",
 ImageSize->{195, 22},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[3]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DiracSimplify", "[", "%", "]"}]], "Input",
 CellLabel->"In[4]:="],

Cell[BoxData[
 GraphicsBox[
  TagBox[RasterBox[CompressedData["
1:eJztnHlMFFcAh7E1bWPT1CNGE0OiRhFURDRVUBBQxGowCtiClLZKEAQVG0BR
TAEBpQoGU1HTBSwgRFEhCKLUq/GoB2CxgoJyCcihUIRdYO+d7rK12mWunePt
zPi+Pwgyk5l532/mMbMjvyn+2z0DPzAzMwv/RPvFc2OkS1jYxt1eo7X/+Co0
PDgodFPAytCITUGbwuz8P9T+0EK36ggzM933CAQCgbwPyFoLMrNzRbGBe+72
akx9MMIGqhYGMEcy9FXsPnj7tZpwPTVUSBeyqukAYxoO005A5Mh7VOKq08FO
zjsud6uGLVO2ZHr53+pFkP7K0CXf3ekzasOKVzcPrlwc80SKDFZHLllb2m2Y
rlpclZd25vLlnJiNCff63l2qkT7/7URu8cXMiHljx062mDHD2nX/U+nbQ+66
Grfeac7kz8dMtZq9YH3Ry+FHzkkwVNMeDl5M7KXAbfCc0BWOkeP7qhoNaV3G
9j0FLZKmYw4LD9bJDZZqui95rTrVrkJkTxPsXM92Gj1F9970c0ttlHYW+8eV
iQ00q3uubVmd2qDdp6w2wdn3jvjtbntvhXuk1st1Z0fGMvdLhgGppZ1dMs1g
VYx3VovS2EMyGZiqaQ+HKCZ2UuA2eE7oCce9ZPihWtlxzsfW774YcwVZfYr3
14fqKM9smq4SjyWJz2QIIr7j67zvqcxgeX9FiFui9qeqtpPOdkPrGYm0Zr97
9L3y7MxHhpYR9cuCVY5JQ8EMPAxzjaoa/G9RzzXPxdFPdKOS1x1y/f4uqgBZ
bbKPqFFh9CGhY3LVdIZDFBOLKVCAddVDEJ66FIUT5Mgt1ego2/MDHMab++BE
oO6rLCio7KX8rKdoOuLgfLJNhQw8ilub8HjQYLF2srdffrFbI2/4xWXmt/fF
xu9H+nivi9+PufWGW0Z0uXhPt8/R7hvp/yve72j926lf3Xl2qf0BXQKy+uPr
Y/+UoG1Z2Zy+wvdKDzNTu+lV0xkOYUzspWA8AFTrIHRCVThBjlxSjTGAF+f2
HC5JmjcNLwJ8IrHp6OgYWkXelLbBZ//p/IzUokapoWRV+ykXS6elfj/sTUpZ
M39N8vmmQfQcMDauRVy+ZXNOC9qvBWlNjPWkhe4xWUWFuZm/d/5vFWX7uWCP
XZkXinJOXHmBcZukbP11mcXKki4GPkDjgGoSw8GUTBwTeykYCxjVZJxQFo6f
I3dUo6NoyYsS1fY1HZuPFYGi61bGZjdHjwPJIrTp8Q3y1pKUpLSco0EWoz6a
4LY1PruJ9B2mprt03bKjTcQ3i6rXZWnhfr4BoRFR+9Ir+0hd6spmkaNdcr3h
hzomgAuqSYApmXRMKABOAZhqOk7eQOWsxoETJ7z8eU5UhvYZU/EcOwIE6b3h
MW3h4cLjTzDnfo24bMcCJ1GzQvtAGWs1YVFehxF6dOHY76zCiVePtCbRwfKb
/DajUtTeUNrP3VlNuHHW4YRqYrAlk40JDbApgFNNx8m/UDqrcQChWtl+1n+F
kwGrtv7x5n/ayBqyorIadTdEuBH0VwRa2kYX/vwA8zlR3XXhS3OboVlSUu4/
yzGdjVcoA5UhUz6btNTTW4tPQGLNAPO7oAKRZD18Uc1RyXqEpVoPR4WTU42B
7FmSs421zRAzzUd9PHr6HJftD/sNVxusjpw1K6Qg9cYrzHfwytaMLybO14pX
d5UGr0uslLDxEqv3ptvEqdsecsS8cfBGNZ8l6+GNaj38F46LsiV9wXT0uV1e
n2Rr6XfmeE7F7avVGK9r1JLHp6NCIo7knS+83jDA0qtx2bNE6/G2KXWsfuTE
PtxWLRDJeritWo+ghA8HJwJpbZzjbM8NXqEZVRKMALpLN1iZj/t05AgtI0fP
C2fpLZZG8uiYv/OiNYE7o2PjU4o7mHoqBQvHVQtDsh6Oq9YjJOGMoui49FN8
frN+xtUoe8oP77r32sTHJFCgamBA1SZG1Zm/Yppr4Sv9rK+W1F09f6VNoLd1
JgaqBgZUbXI0/VVJa60mms918wnadUBU8OBv/vxJDc+AqoEBVUMgEAgEAoFA
IBAIBAKBQCDMAHtBQQJtgwTaNiGwShck0DZIoG08aFR0koB6la4AC29xVTPR
d0qvuBgraD6q1sNuuyxV2zinAX9Vo0KtopMYGlW6wiy8xVbNQN8pzeJizKD5
qprddll6tjFOA4CqgVSDUqvoJIJWla4QC291YKmm3XdKt7iYIGgeqmazXZau
bZwrjmHV6ACqBqVU0UkInSpdQRbe6sBQTb/vlG5xMX7QfFTNZrssXds4Vxyj
qtEBVQ1KsaITb0dDG6dTpctk4a3qZXHQtjJchSZXbVzfKdO2CYPmXbcwk+2y
zNvGueKYVI0OF1pYyVV0UukFZaKPlCyqF9nL3a/j/P0rF1SThhXbwLpYgalm
aERcP7eNhhMtrKQqOin1gjLQR0oegomFE6rJwo5tULW34FQzMyLun9tGwqNq
UI72giLvVoPaW44ZZ7MYtrCyhhALbxHO2qYOn6pBedALinfHwifVCC9sY8Iz
1Qi/bRPB+WpQHvSCEn7GoofzqhFe2CYDH1QjgrGNCverQbnfC0p/YuGIaoQP
tsnAC9WIUGwzDawGBQZUDQyo2sTAalBgQNXAgKpNDqwGBQZUDQyoGgKBQADz
D6YX9vU=
    "], {{0, 38}, {371, 0}}, {0, 255},
    ColorFunction->RGBColor],
   BoxForm`ImageTag["Byte", ColorSpace -> "RGB", Interleaving -> True],
   Selectable->False],
  DefaultBaseStyle->"ImageGraphics",
  ImageSize->Automatic,
  ImageSizeRaw->{371, 38},
  PlotRange->{{0, 371}, {0, 38}}]], "Output",
 ImageSize->{375, 38},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"RasterizedOutput",
 CellLabel->"Out[4]=",
 CellID->745659537]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DiracTrace", "[", 
  RowBox[{"GA", "[", 
   RowBox[{
   "\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Sigma]", ",", "\[Delta]", 
    ",", "\[Tau]", ",", "6"}], "]"}], "]"}]], "Input",
 CellLabel->"In[5]:="],

Cell[BoxData[
 FormBox[
  RowBox[{"tr", "(", 
   FormBox[
    RowBox[{
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox[
        FormBox["\[Mu]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox[
        FormBox["\[Nu]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox[
        FormBox["\[Rho]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox[
        FormBox["\[Sigma]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox[
        FormBox["\[Delta]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox[
        FormBox["\[Tau]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox["6",
        TraditionalForm]],
      TraditionalForm]}],
    TraditionalForm], ")"}], TraditionalForm]], "Output",
 ImageSize->{195, 21},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[5]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DiracSimplify", "[", "%", "]"}]], "Input",
 CellLabel->"In[6]:="],

Cell[BoxData[
 GraphicsBox[
  TagBox[RasterBox[CompressedData["
1:eJztnQuMVdUVhrE1TWvbKBojiTFRYxHqAx+pMgLyFKvBKmALUtoKURBUbAHB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    "], {{0, 118}, {
    536, 0}}, {0, 255},
    ColorFunction->RGBColor],
   BoxForm`ImageTag["Byte", ColorSpace -> "RGB", Interleaving -> True],
   Selectable->False],
  DefaultBaseStyle->"ImageGraphics",
  ImageSize->Automatic,
  ImageSizeRaw->{536, 118},
  PlotRange->{{0, 536}, {0, 118}}]], "Output",
 ImageSize->{540, 118},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"RasterizedOutput",
 CellLabel->"Out[6]=",
 CellID->837611303]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 InterpretationBox[Cell["\t", "ExampleDelimiter"],
  $Line = 0; Null]], "ExampleDelimiter"],

Cell[TextData[{
 Cell[BoxData["D"], "InlineFormula"],
 "-dimensional traces that do not involve ",
 Cell[BoxData[
  SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"],
 " are unambiguous."
}], "Notes"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"DiracTrace", "[", 
   RowBox[{
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", 
       RowBox[{"GSD", "[", "q", "]"}]}], "+", 
      RowBox[{"SMP", "[", "\"\<m_e\>\"", "]"}]}], ")"}], ".", 
    RowBox[{"GAD", "[", "\[Nu]", "]"}], ".", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"GSD", "[", 
       RowBox[{"p", "-", "q"}], "]"}], "+", 
      RowBox[{"SMP", "[", "\"\<m_e\>\"", "]"}]}], ")"}], ".", 
    RowBox[{"GAD", "[", "\[Mu]", "]"}]}], "]"}], " "}]], "Input",
 CellLabel->"In[1]:="],

Cell[BoxData[
 FormBox[
  RowBox[{"tr", "(", 
   FormBox[
    RowBox[{
     RowBox[{"(", 
      RowBox[{
       SubscriptBox["m", "e"], "-", 
       FormBox[
        RowBox[{"\[Gamma]", "\[CenterDot]", 
         FormBox[
          FormBox["q",
           TraditionalForm],
          TraditionalForm]}],
        TraditionalForm]}], ")"}], ".", 
     FormBox[
      SuperscriptBox["\[Gamma]", 
       FormBox[
        FormBox["\[Nu]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     RowBox[{"(", 
      RowBox[{
       SubscriptBox["m", "e"], "+", 
       FormBox[
        RowBox[{"\[Gamma]", "\[CenterDot]", "(", 
         FormBox[
          FormBox[
           RowBox[{
            FormBox["p",
             TraditionalForm], "-", 
            FormBox["q",
             TraditionalForm]}],
           TraditionalForm],
          TraditionalForm], ")"}],
        TraditionalForm]}], ")"}], ".", 
     FormBox[
      SuperscriptBox["\[Gamma]", 
       FormBox[
        FormBox["\[Mu]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm]}],
    TraditionalForm], ")"}], TraditionalForm]], "Output",
 ImageSize->{280, 19},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[1]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DiracSimplify", "[", "%", "]"}]], "Input",
 CellLabel->"In[2]:="],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"4", " ", 
    SubsuperscriptBox["m", "e", "2"], " ", 
    SuperscriptBox["g", 
     RowBox[{
      FormBox[
       FormBox["\[Mu]",
        TraditionalForm],
       TraditionalForm], 
      FormBox[
       FormBox["\[Nu]",
        TraditionalForm],
       TraditionalForm]}]]}], "+", 
   RowBox[{"4", " ", 
    SuperscriptBox["g", 
     RowBox[{
      FormBox[
       FormBox["\[Mu]",
        TraditionalForm],
       TraditionalForm], 
      FormBox[
       FormBox["\[Nu]",
        TraditionalForm],
       TraditionalForm]}]], " ", 
    RowBox[{"(", 
     RowBox[{
      FormBox[
       FormBox["p",
        TraditionalForm],
       TraditionalForm], 
      FormBox["\<\"\[CenterDot]\"\>",
       TraditionalForm], 
      FormBox[
       FormBox["q",
        TraditionalForm],
       TraditionalForm]}], ")"}]}], "-", 
   RowBox[{"4", " ", 
    SuperscriptBox[
     FormBox[
      FormBox["q",
       TraditionalForm],
      TraditionalForm], "2"], " ", 
    SuperscriptBox["g", 
     RowBox[{
      FormBox[
       FormBox["\[Mu]",
        TraditionalForm],
       TraditionalForm], 
      FormBox[
       FormBox["\[Nu]",
        TraditionalForm],
       TraditionalForm]}]]}], "-", 
   RowBox[{"4", " ", 
    SuperscriptBox[
     FormBox[
      FormBox["p",
       TraditionalForm],
      TraditionalForm], 
     FormBox[
      FormBox["\[Nu]",
       TraditionalForm],
      TraditionalForm]], " ", 
    SuperscriptBox[
     FormBox[
      FormBox["q",
       TraditionalForm],
      TraditionalForm], 
     FormBox[
      FormBox["\[Mu]",
       TraditionalForm],
      TraditionalForm]]}], "-", 
   RowBox[{"4", " ", 
    SuperscriptBox[
     FormBox[
      FormBox["p",
       TraditionalForm],
      TraditionalForm], 
     FormBox[
      FormBox["\[Mu]",
       TraditionalForm],
      TraditionalForm]], " ", 
    SuperscriptBox[
     FormBox[
      FormBox["q",
       TraditionalForm],
      TraditionalForm], 
     FormBox[
      FormBox["\[Nu]",
       TraditionalForm],
      TraditionalForm]]}], "+", 
   RowBox[{"8", " ", 
    SuperscriptBox[
     FormBox[
      FormBox["q",
       TraditionalForm],
      TraditionalForm], 
     FormBox[
      FormBox["\[Mu]",
       TraditionalForm],
      TraditionalForm]], " ", 
    SuperscriptBox[
     FormBox[
      FormBox["q",
       TraditionalForm],
      TraditionalForm], 
     FormBox[
      FormBox["\[Nu]",
       TraditionalForm],
      TraditionalForm]]}]}], TraditionalForm]], "Output",
 ImageSize->{482, 19},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[2]="]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 InterpretationBox[Cell["\t", "ExampleDelimiter"],
  $Line = 0; Null]], "ExampleDelimiter"],

Cell[TextData[{
 "Traces that contain ",
 Cell[BoxData[
  SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"],
 " in ",
 Cell[BoxData["D"], "InlineFormula"],
 "-dimensions are scheme-dependent. The default scheme used in FeynCalc is \
the naive dimension regularization (NDR), where ",
 Cell[BoxData[
  SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"],
 " is assumed to anticommute with all other Dirac matrices. However, chiral \
traces are ambiguous NDR, unless the trace contains an even number of ",
 Cell[BoxData[
  SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"],
 ". This is why FeynCalc will leave such traces unevaluated."
}], "Notes"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DiracTrace", "[", 
  RowBox[{
   RowBox[{"GAD", "[", 
    RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]"}], "]"}], ".", 
   RowBox[{"GA", "[", "5", "]"}], ".", 
   RowBox[{"GAD", "[", 
    RowBox[{"\[Sigma]", ",", "\[Delta]", ",", "\[Tau]"}], "]"}], ".", 
   RowBox[{"GA", "[", "5", "]"}]}], "]"}]], "Input",
 CellLabel->"In[1]:="],

Cell[BoxData[
 FormBox[
  RowBox[{"tr", "(", 
   FormBox[
    RowBox[{
     FormBox[
      SuperscriptBox["\[Gamma]", 
       FormBox[
        FormBox["\[Mu]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox["\[Gamma]", 
       FormBox[
        FormBox["\[Nu]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox["\[Gamma]", 
       FormBox[
        FormBox["\[Rho]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox["5",
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox["\[Gamma]", 
       FormBox[
        FormBox["\[Sigma]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox["\[Gamma]", 
       FormBox[
        FormBox["\[Delta]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox["\[Gamma]", 
       FormBox[
        FormBox["\[Tau]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox["5",
        TraditionalForm]],
      TraditionalForm]}],
    TraditionalForm], ")"}], TraditionalForm]], "Output",
 ImageSize->{213, 22},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[1]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DiracSimplify", "[", "%", "]"}]], "Input",
 CellLabel->"In[2]:="],

Cell[BoxData[
 GraphicsBox[
  TagBox[RasterBox[CompressedData["
1:eJztnX1sldUdx9lmtsX9MdQsmixN3CIoboiDDOl4aSsVBmGTFxcL6TZpxA51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    "], {{0, 78}, {512, 0}}, {0, 255},
    ColorFunction->RGBColor],
   BoxForm`ImageTag["Byte", ColorSpace -> "RGB", Interleaving -> True],
   Selectable->False],
  DefaultBaseStyle->"ImageGraphics",
  ImageSize->Automatic,
  ImageSizeRaw->{512, 78},
  PlotRange->{{0, 512}, {0, 78}}]], "Output",
 ImageSize->{516, 78},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"RasterizedOutput",
 CellLabel->"Out[2]=",
 CellID->249793213]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DiracTrace", "[", 
  RowBox[{
   RowBox[{"GAD", "[", 
    RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]"}], "]"}], ".", 
   RowBox[{"GA", "[", "5", "]"}], ".", 
   RowBox[{"GAD", "[", 
    RowBox[{"\[Sigma]", ",", "\[Delta]", ",", "\[Tau]"}], "]"}], ".", 
   RowBox[{"GA", "[", "7", "]"}]}], "]"}]], "Input",
 CellLabel->"In[3]:="],

Cell[BoxData[
 FormBox[
  RowBox[{"tr", "(", 
   FormBox[
    RowBox[{
     FormBox[
      SuperscriptBox["\[Gamma]", 
       FormBox[
        FormBox["\[Mu]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox["\[Gamma]", 
       FormBox[
        FormBox["\[Nu]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox["\[Gamma]", 
       FormBox[
        FormBox["\[Rho]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox["5",
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox["\[Gamma]", 
       FormBox[
        FormBox["\[Sigma]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox["\[Gamma]", 
       FormBox[
        FormBox["\[Delta]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox["\[Gamma]", 
       FormBox[
        FormBox["\[Tau]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox["7",
        TraditionalForm]],
      TraditionalForm]}],
    TraditionalForm], ")"}], TraditionalForm]], "Output",
 ImageSize->{213, 22},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[3]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DiracSimplify", "[", "%", "]"}]], "Input",
 CellLabel->"In[4]:="],

Cell[BoxData[
 GraphicsBox[
  TagBox[RasterBox[CompressedData["
1:eJztnQlUVFeax81MTp+ZZM5J1OkTZ2wn0RgNJi4RO0pUQEFcYtp1juLRtHI6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    "], {{0, 119}, {512, 0}}, {0, 255},
    ColorFunction->RGBColor],
   BoxForm`ImageTag["Byte", ColorSpace -> "RGB", Interleaving -> True],
   Selectable->False],
  DefaultBaseStyle->"ImageGraphics",
  ImageSize->Automatic,
  ImageSizeRaw->{512, 119},
  PlotRange->{{0, 512}, {0, 119}}]], "Output",
 ImageSize->{516, 119},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"RasterizedOutput",
 CellLabel->"Out[4]=",
 CellID->715016264]
}, Open  ]],

Cell[TextData[{
 "Over the years people invented many different schemes to deal with ",
 Cell[BoxData[
  SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"],
 " in dimensional regularization. Currently, only the \
t'Hooft-Veltman-Breitenlohner-Maison  (BMHV) prescription is fully supported \
in FeynCalc."
}], "Notes"],

Cell[BoxData[
 RowBox[{
  RowBox[{"FCSetDiracGammaScheme", "[", "\"\<BMHV\>\"", "]"}], ";"}]], "Input",\

 CellLabel->"In[5]:="],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DiracSimplify", "[", 
  RowBox[{"DiracTrace", "[", 
   RowBox[{
    RowBox[{"GAD", "[", 
     RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]"}], "]"}], ".", 
    RowBox[{"GA", "[", "5", "]"}], ".", 
    RowBox[{"GAD", "[", 
     RowBox[{"\[Sigma]", ",", "\[Delta]", ",", "\[Tau]"}], "]"}], ".", 
    RowBox[{"GA", "[", "7", "]"}]}], "]"}], "]"}]], "Input",
 CellLabel->"In[6]:="],

Cell[BoxData[
 GraphicsBox[
  TagBox[RasterBox[CompressedData["
1:eJztnXt0VVWe53Wm1/Q01a7ysagGWaxqEaoiqOmUxUMMFD4ay54CBHqAFsYH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    "], {{0, 458}, {516, 0}}, {0, 255},
    ColorFunction->RGBColor],
   BoxForm`ImageTag["Byte", ColorSpace -> "RGB", Interleaving -> True],
   Selectable->False],
  DefaultBaseStyle->"ImageGraphics",
  ImageSize->Automatic,
  ImageSizeRaw->{516, 458},
  PlotRange->{{0, 516}, {0, 458}}]], "Output",
 ImageSize->{520, 458},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"RasterizedOutput",
 CellLabel->"Out[6]=",
 CellID->253055425]
}, Open  ]],

Cell[TextData[{
 "Keep in mind that the BMHV scheme violates axial Ward identities and \
requires special model-dependent counter-terms to restore those. Therefore, \
just setting ",
 ButtonBox["FCSetDiracGammaScheme[\"BMHV\"]",
  BaseStyle->"Link",
  ButtonData->"paclet:FeynCalc/ref/FCSetDiracGammaScheme",
  ButtonNote->"FCSetDiracGammaScheme"],
 " does not automatically resolve all your troubles with ",
 Cell[BoxData[
  SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"],
 " in ",
 Cell[BoxData["D"], "InlineFormula"],
 "-dimensions. The proper treatment of ",
 Cell[BoxData[
  SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"],
 " in dimensional regularization is an intricate issue that cannot be boiled \
down to a simple and universal recipe. FeynCalc merely carries out the \
algebraic operations that you request, but it is still your task to ensure \
that what you do makes sense."
}], "Notes"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 InterpretationBox[Cell["\t", "ExampleDelimiter"],
  $Line = 0; Null]], "ExampleDelimiter"],

Cell[TextData[{
 "Traces that are free of  ",
 Cell[BoxData[
  SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"],
 " but contain both ",
 Cell[BoxData["4"], "InlineFormula"],
 "- and ",
 Cell[BoxData["D"], "InlineFormula"],
 "-dimensional Dirac matrices may appear in calculations that use the BMHV \
prescription, but they do not make sense in NDR. Therefore, their evaluation \
will be succesful only if the correct scheme is used."
}], "Notes"],

Cell[BoxData[
 RowBox[{
  RowBox[{"FCSetDiracGammaScheme", "[", "\"\<NDR\>\"", "]"}], ";"}]], "Input",\

 CellLabel->"In[1]:="],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"DiracTrace", "[", 
   RowBox[{
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", 
       RowBox[{"GSD", "[", "q", "]"}]}], "+", 
      RowBox[{"SMP", "[", "\"\<m_e\>\"", "]"}]}], ")"}], ".", 
    RowBox[{"GA", "[", "\[Nu]", "]"}], ".", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"GS", "[", "p", "]"}], "-", 
      RowBox[{"GSD", "[", "q", "]"}], "+", 
      RowBox[{"SMP", "[", "\"\<m_e\>\"", "]"}]}], ")"}], ".", 
    RowBox[{"GA", "[", "\[Mu]", "]"}]}], "]"}], " "}]], "Input",
 CellLabel->"In[2]:="],

Cell[BoxData[
 FormBox[
  RowBox[{"tr", "(", 
   FormBox[
    RowBox[{
     RowBox[{"(", 
      RowBox[{
       SubscriptBox["m", "e"], "-", 
       FormBox[
        RowBox[{"\[Gamma]", "\[CenterDot]", 
         FormBox[
          FormBox["q",
           TraditionalForm],
          TraditionalForm]}],
        TraditionalForm]}], ")"}], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox[
        FormBox["\[Nu]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     RowBox[{"(", 
      RowBox[{
       FormBox[
        RowBox[{
         OverscriptBox["\[Gamma]", "_"], "\[CenterDot]", 
         FormBox[
          OverscriptBox[
           FormBox["p",
            TraditionalForm], "_"],
          TraditionalForm]}],
        TraditionalForm], "+", 
       SubscriptBox["m", "e"], "-", 
       FormBox[
        RowBox[{"\[Gamma]", "\[CenterDot]", 
         FormBox[
          FormBox["q",
           TraditionalForm],
          TraditionalForm]}],
        TraditionalForm]}], ")"}], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox[
        FormBox["\[Mu]",
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm]}],
    TraditionalForm], ")"}], TraditionalForm]], "Output",
 ImageSize->{292, 19},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[2]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DiracSimplify", "[", "%", "]"}]], "Input",
 CellLabel->"In[3]:="],

Cell[BoxData[
 FormBox[
  RowBox[{
   StyleBox[
    RowBox[{"DiracTrace", "::", "mixmsg"}], "MessageName"], ":", 
   " ", "\<\"Expressions that mix D-, 4- and D-4-dimensional quantities are \
forbidden in Dirac matrix chains unless you are using the t'Hooft-Veltman \
scheme. For every other scheme, please recheck your input expressions and \
ensure that all matrices, spinors and tensors are purely D-dimensional. You \
might want to use FCGetDimensions[exp] to find the offending terms and fix \
them by hand or ChangeDimension[exp,D] to convert the whole expression to \
D-dimensions. If you explicitly intend to use the t'Hooft-Veltman scheme, \
please activate it via FCSetDiracGammaScheme[\\\"BMHV\\\"]. \
\\!\\(\\*ButtonBox[\\\"\[RightSkeleton]\\\", ButtonStyle->\\\"Link\\\", \
ButtonFrame->None, ButtonData:>\\\"paclet:FeynCalc/ref/DiracTrace\\\", \
ButtonNote -> \\\"FeynCalc`DiracTrace::mixmsg\\\"]\\)\"\>"}], 
  TraditionalForm]], "Message", "MSG",
 CellLabel->"During evaluation of In[3]:="],

Cell[BoxData[
 FormBox["$Aborted", TraditionalForm]], "Output",
 ImageSize->{58, 14},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[3]="]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"FCSetDiracGammaScheme", "[", "\"\<BMHV\>\"", "]"}], ";"}]], "Input",\

 CellLabel->"In[4]:="],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DiracSimplify", "[", 
  RowBox[{"DiracTrace", "[", 
   RowBox[{
    RowBox[{"(", 
     RowBox[{
      RowBox[{"-", 
       RowBox[{"GSD", "[", "q", "]"}]}], "+", 
      RowBox[{"SMP", "[", "\"\<m_e\>\"", "]"}]}], ")"}], ".", 
    RowBox[{"GA", "[", "\[Nu]", "]"}], ".", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"GS", "[", "p", "]"}], "-", 
      RowBox[{"GSD", "[", "q", "]"}], "+", 
      RowBox[{"SMP", "[", "\"\<m_e\>\"", "]"}]}], ")"}], ".", 
    RowBox[{"GA", "[", "\[Mu]", "]"}]}], "]"}], " ", "]"}]], "Input",
 CellLabel->"In[5]:="],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"4", " ", 
    SubsuperscriptBox["m", "e", "2"], " ", 
    SuperscriptBox[
     OverscriptBox["g", "_"], 
     RowBox[{
      FormBox[
       FormBox["\[Mu]",
        TraditionalForm],
       TraditionalForm], 
      FormBox[
       FormBox["\[Nu]",
        TraditionalForm],
       TraditionalForm]}]]}], "+", 
   RowBox[{"4", " ", 
    SuperscriptBox[
     OverscriptBox["g", "_"], 
     RowBox[{
      FormBox[
       FormBox["\[Mu]",
        TraditionalForm],
       TraditionalForm], 
      FormBox[
       FormBox["\[Nu]",
        TraditionalForm],
       TraditionalForm]}]], " ", 
    RowBox[{"(", 
     RowBox[{
      FormBox[
       OverscriptBox[
        FormBox["p",
         TraditionalForm], "_"],
       TraditionalForm], 
      FormBox["\<\"\[CenterDot]\"\>",
       TraditionalForm], 
      FormBox[
       OverscriptBox[
        FormBox["q",
         TraditionalForm], "_"],
       TraditionalForm]}], ")"}]}], "-", 
   RowBox[{"4", " ", 
    SuperscriptBox[
     FormBox[
      FormBox["q",
       TraditionalForm],
      TraditionalForm], "2"], " ", 
    SuperscriptBox[
     OverscriptBox["g", "_"], 
     RowBox[{
      FormBox[
       FormBox["\[Mu]",
        TraditionalForm],
       TraditionalForm], 
      FormBox[
       FormBox["\[Nu]",
        TraditionalForm],
       TraditionalForm]}]]}], "-", 
   RowBox[{"4", " ", 
    SuperscriptBox[
     FormBox[
      OverscriptBox[
       FormBox["p",
        TraditionalForm], "_"],
      TraditionalForm], 
     FormBox[
      FormBox["\[Nu]",
       TraditionalForm],
      TraditionalForm]], " ", 
    SuperscriptBox[
     FormBox[
      OverscriptBox[
       FormBox["q",
        TraditionalForm], "_"],
      TraditionalForm], 
     FormBox[
      FormBox["\[Mu]",
       TraditionalForm],
      TraditionalForm]]}], "-", 
   RowBox[{"4", " ", 
    SuperscriptBox[
     FormBox[
      OverscriptBox[
       FormBox["p",
        TraditionalForm], "_"],
      TraditionalForm], 
     FormBox[
      FormBox["\[Mu]",
       TraditionalForm],
      TraditionalForm]], " ", 
    SuperscriptBox[
     FormBox[
      OverscriptBox[
       FormBox["q",
        TraditionalForm], "_"],
      TraditionalForm], 
     FormBox[
      FormBox["\[Nu]",
       TraditionalForm],
      TraditionalForm]]}], "+", 
   RowBox[{"8", " ", 
    SuperscriptBox[
     FormBox[
      OverscriptBox[
       FormBox["q",
        TraditionalForm], "_"],
      TraditionalForm], 
     FormBox[
      FormBox["\[Mu]",
       TraditionalForm],
      TraditionalForm]], " ", 
    SuperscriptBox[
     FormBox[
      OverscriptBox[
       FormBox["q",
        TraditionalForm], "_"],
      TraditionalForm], 
     FormBox[
      FormBox["\[Nu]",
       TraditionalForm],
      TraditionalForm]]}]}], TraditionalForm]], "Output",
 ImageSize->{504, 19},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[5]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"%", "//", "FCE"}], "//", "StandardForm"}]], "Input",
 CellLabel->"In[6]:="],

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"-", "4"}], " ", 
   RowBox[{"FV", "[", 
    RowBox[{"p", ",", "\[Nu]"}], "]"}], " ", 
   RowBox[{"FV", "[", 
    RowBox[{"q", ",", "\[Mu]"}], "]"}]}], "-", 
  RowBox[{"4", " ", 
   RowBox[{"FV", "[", 
    RowBox[{"p", ",", "\[Mu]"}], "]"}], " ", 
   RowBox[{"FV", "[", 
    RowBox[{"q", ",", "\[Nu]"}], "]"}]}], "+", 
  RowBox[{"8", " ", 
   RowBox[{"FV", "[", 
    RowBox[{"q", ",", "\[Mu]"}], "]"}], " ", 
   RowBox[{"FV", "[", 
    RowBox[{"q", ",", "\[Nu]"}], "]"}]}], "+", 
  RowBox[{"4", " ", 
   RowBox[{"MT", "[", 
    RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}], " ", 
   SuperscriptBox[
    RowBox[{"SMP", "[", "\<\"m_e\"\>", "]"}], "2"]}], "+", 
  RowBox[{"4", " ", 
   RowBox[{"MT", "[", 
    RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}], " ", 
   RowBox[{"SP", "[", 
    RowBox[{"p", ",", "q"}], "]"}]}], "-", 
  RowBox[{"4", " ", 
   RowBox[{"MT", "[", 
    RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}], " ", 
   RowBox[{"SPD", "[", 
    RowBox[{"q", ",", "q"}], "]"}]}]}]], "Output",
 ImageSize->{508, 34},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[6]//StandardForm="]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"FCSetDiracGammaScheme", "[", "\"\<NDR\>\"", "]"}], ";"}]], "Input",\

 CellLabel->"In[7]:="],

Cell[TextData[{
 "Notice that in this case the result contains ",
 Cell[BoxData["4"], "InlineFormula"],
 "- and ",
 Cell[BoxData["D"], "InlineFormula"],
 "-dimensional tensors."
}], "Notes"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 InterpretationBox[Cell["\t", "ExampleDelimiter"],
  $Line = 0; Null]], "ExampleDelimiter"],

Cell[TextData[{
 "Traces involving ",
 Cell[BoxData[
  SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"],
 " in the BMHV scheme are evaluated using West's formula. It is possible to \
turn it off by setting the option ",
 ButtonBox["West",
  BaseStyle->"Link",
  ButtonData->"paclet:FeynCalc/ref/West",
  ButtonNote->"West"],
 " to ",
 Cell[BoxData["False"], "InlineFormula"],
 ", but then the evaluation will require much more time."
}], "Notes"],

Cell[BoxData[
 RowBox[{
  RowBox[{"FCSetDiracGammaScheme", "[", "\"\<BMHV\>\"", "]"}], ";"}]], "Input",\

 CellLabel->"In[1]:="],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"AbsoluteTiming", "[", 
  RowBox[{
   RowBox[{"r1", "=", 
    RowBox[{"DiracSimplify", "[", 
     RowBox[{"DiracTrace", "[", 
      RowBox[{
       RowBox[{"GAD", "[", 
        RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]"}], "]"}], ".", 
       RowBox[{"GA", "[", "5", "]"}], ".", 
       RowBox[{"GAD", "[", 
        RowBox[{"\[Sigma]", ",", "\[Delta]", ",", "\[Tau]"}], "]"}], ".", 
       RowBox[{"GA", "[", "7", "]"}]}], "]"}], "]"}]}], ";"}], "]"}]], "Input",\

 CellLabel->"In[2]:="],

Cell[BoxData[
 FormBox[
  RowBox[{"{", 
   RowBox[{"0.211407`", ",", "Null"}], "}"}], TraditionalForm]], "Output",
 ImageSize->{105, 16},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[2]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"AbsoluteTiming", "[", 
  RowBox[{
   RowBox[{"r2", "=", 
    RowBox[{"DiracSimplify", "[", 
     RowBox[{"DiracTrace", "[", 
      RowBox[{
       RowBox[{
        RowBox[{"GAD", "[", 
         RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]"}], "]"}], ".", 
        RowBox[{"GA", "[", "5", "]"}], ".", 
        RowBox[{"GAD", "[", 
         RowBox[{"\[Sigma]", ",", "\[Delta]", ",", "\[Tau]"}], "]"}], ".", 
        RowBox[{"GA", "[", "7", "]"}]}], ",", 
       RowBox[{"West", "\[Rule]", "False"}]}], "]"}], "]"}]}], ";"}], 
  "]"}]], "Input",
 CellLabel->"In[3]:="],

Cell[BoxData[
 FormBox[
  RowBox[{"{", 
   RowBox[{"2.041849`", ",", "Null"}], "}"}], TraditionalForm]], "Output",
 ImageSize->{98, 16},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[3]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"r1", "===", "r2"}]], "Input",
 CellLabel->"In[4]:="],

Cell[BoxData[
 FormBox["True", TraditionalForm]], "Output",
 ImageSize->{31, 14},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[4]="]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"FCSetDiracGammaScheme", "[", "\"\<NDR\>\"", "]"}], ";"}]], "Input",\

 CellLabel->"In[5]:="],

Cell[BoxData[
 RowBox[{"ClearAll", "[", 
  RowBox[{"r1", ",", "r2"}], "]"}]], "Input",
 CellLabel->"In[6]:="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 InterpretationBox[Cell["\t", "ExampleDelimiter"],
  $Line = 0; Null]], "ExampleDelimiter"],

Cell[TextData[{
 "If you know that traces with one ",
 Cell[BoxData[
  SuperscriptBox["\[Gamma]", "5"]], "InlineFormula"],
 " ",
 " do not contribute to your final result, use the new NDR-Discard scheme to \
put them to zero"
}], "ExampleText",
 CellID->2003592022],

Cell[BoxData[
 RowBox[{
  RowBox[{"FCSetDiracGammaScheme", "[", "\"\<NDR-Discard\>\"", "]"}], 
  ";"}]], "Input",
 CellLabel->"In[1]:="],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DiracSimplify", "[", 
  RowBox[{"DiracTrace", "[", 
   RowBox[{
    RowBox[{"GAD", "[", 
     RowBox[{"\[Mu]", ",", "\[Nu]", ",", "\[Rho]"}], "]"}], ".", 
    RowBox[{"GA", "[", "5", "]"}], ".", 
    RowBox[{"GAD", "[", 
     RowBox[{"\[Sigma]", ",", "\[Delta]", ",", "\[Tau]"}], "]"}], ".", 
    RowBox[{"GA", "[", "7", "]"}]}], "]"}], "]"}]], "Input",
 CellLabel->"In[2]:="],

Cell[BoxData[
 GraphicsBox[
  TagBox[RasterBox[CompressedData["
1:eJztnQ1sVeUZgMtmls0tUTSLJIZEzQZ2m2I0Uzp+Wn6EQVD50QiEbdIMuwKD
jaKiZhaBwaBsLJHup1gtUCaMQfiRnwFqgqwyyuZPAcECHSCl2Aqlhd7+3HvP
7r3VQMs95/vOPe/3ft/39n0SDX85773Pec/JaXuT587smWOf/kpaWlre12P/
Gzv5uUGzZk1+ftzNsd88MSMvN2fGlJ+PmDF7Ss6UWX2zvxr7w0dj/6XF/n38
1w7DMAzDBKf5zMaSVWuK5j794nv1Ud0vpkvB5nXB5hmmnUsHn1+y72IEZ1iE
r7aroJpvh/0nkDXPuhjihBsq1uZmZj2zqy7c4Y9r98ybkHnvHTd1vyv9Bw9O
2HI+7HYAEW2nS8Zlv1vvOJffnzHwp2WXOv5tNPS/f762Zuv2ktn333LLHb16
975n6MJjoRTGtH62d8mIfvlHQk7ToecGjt5Z1/nSjTRUrFvx9127SvMnL9h/
yYAL28U8oJMEXv5BzjIh845oXWVBcSLYE7hLmCFKqLJ45osbTzdW/an/Q0sq
W67+RSRUU9scbarIf3Ll6bZAI6J1O8aNfKM67DQfW9B36PqaDg9d0fp388Ys
P94Sv+yKh4zacd1l4ov6vZOGLT8ZqtmaPe9AQ6cjRS68Ne2R5Sdik5qPLsia
WNYQZBAAruaBnXj6BzvLNMzH8VxXX6h2ItoTuEuYMY5oU+XqGYN7fftb3e/s
P23lJ00p3SOitdvGDFz0SbPjNJRNzPrtseZOf998dOn4opOtwV7p5YNThy2K
HTp8dnVW38Swa7jw1th+Lx2JP7K0VP5+6M/eC3ZvCH28cNRL+8tXlXzU+Xpz
Iuc3jhxQkLjar3wwa+gLFU2pDlFuHtaJt/84EGeZhvk4Ql3SqHYitScglzBj
Gk1H/jCzcP/5ltbPDxY+2uOmPtc/x8jQWvVK/6zVZ8POlY/mjV5wuPMStp16
dfjE3ReCPX7GHqMyHt5eF2058ddB3/vJvxs6PE9FatYPzlgcf+3Nx/88Ye5/
GwONckKHXx406Tdrjie5mhrKnvxuRmnsrTqXP5w/qfB4KroSKDcP7MTTfxyQ
s0zCfByhLnkUO5HaE5CTy5hGa807e859sTRXPph+1+2P7Evp+5QtVSueGr9w
7Ybi5VtOhq5bkrYzrw/pNWJbbZAfUIar3xh0d+bgSb96uWDZYw88tnRzVYfH
trbqf+SOmVPy5pbS13Z/GuBZq52G8mm/KD2d7GEn9HH+Pbc/NCp/5ZZNa0re
qfF8Hgqf35rzywMuT90I5kGdCPw7MGcZyLwnKDsv1iWPaicyewJychmTaSyf
nJ7xl1NeS9RyZtuyghWlhTm9bvzabcOmz19VlfIPE30eP1q38/EhhVWAX3+m
9F7aThUN6LtU8jEr/Omqh0e9fVH8Dw0wL5oC6V+9eWlUmfetC8EJzgoxdhK9
uHfqkLx9Hh9ijjYceObBzKLYxdJ8dG76bT9adw72YcDr+PHrKePZ1L/j62eW
B7Gv+TPue/aQ5MuQvP/rNy+eAucfxbzsa1Fl3qcuBCc4K8RYSqS+bNGvi496
fY0aqX3zxz37JJ42Gsuzvz/gVeDPAqg+Ptqstur12cMz42Tc3f3WPv0Svxw5
/V/JbzMGmCcz5ar5a2DzCCP8mWeMItpU+bfFxR9e9+GCjrSdKf5hjwdiixOp
3Zn7+KL3G4FPrerj488SP/+bYZ7eFDFdzLwp2hnjaDmzZVnRgfrEl4OR+kOb
dlQn/35ipPHw2hemzn5l3eZNb5+4Ar8/qo+PP0t0/zfFPL0pIrqceTO0M6YR
rt2e2/sb3dK+oNuN9xYk/3FSpG7nU+k9b/3mDd1i3HDz/XlBP06IfHwdszzv
/8aYpzdFQNczb4R2xl5az+343fwNp9o/GxZtu1D+xzn7JT7XYszxdc0KDs6r
pTQFCjJO7NLOGEe4ZsPw7wzd9Fn7JwYijZV7Nu8+G/gz9njH1zUrODivltIU
KMg4sUs7YyDRyxUFo9N79Lxv2PicOYuLNv7nc9gPD6g+vq5ZwcF5tZSmQEHG
iV3aGYZhGIZhGIZhGIZhGIZhGIZhGGvgUqou2Lwu2Lwu2LxpcB1YF9h1YJb/
Jdxl1gXvvGForgPHCV5K9YyxwsZ24fBq1EIVdfWmga0zj9dlbkfp5ptYB9a9
8zg5chPNJ0V3HTgxCqYe6xZjBY7tQuHdqIUq6mpNA1tnHrHLnEDt5ptXB9a/
8zg5cgTzROrADlw91i3GChzbRTEPVtTVmga2zjxyl1n15seBqQPT2Xm0HLna
LjOROnAcqHqsS4wVOLaLYx7KidY0sHXmsbvMijc/DkwdmM7O4+XIlXaZydSB
AeuxbjFW2AAxinkoJ5rTwNaZx+0yK998R/786i5io+08Vo4cxrwMBjRqA9Rp
bS6lqjIP5UR7GlgZBuy8aIpdm6+9iG3izotmgSBtPjn6G7WB6rQWl1KVmYdy
oj0NrAr9Oy+eYtnm6y5im7fz4lkwBLr/G1BKRasDm1VKNcA8zgiEKTaaR5ui
dJCNRWwaOXJ/5pNiRikVLWBqUCnVDPM4I9CmSGGMebQpOIMsKmITy5Gn+vxv
SikVLWBqTCnVFPM4I9CmSGCQebQpOIMsKmITy5GndP83ppSKFjA1pZRqjHmc
EWhTxJhkHm0K1iBritjkcuQBf/7rCZk6sHWlVDL1WDavcQrmoOCQ2Xn8WUog
Uwe2rpRKph7L5jVOwRwUHDI7jz9LEWTqwNaVUsnUY9m8ximYg4JDZufxZzEM
wzAMwzAMwzAMwzAMwzAMwwDDRU5dsHldsHldsHnT4P6vLti8LmTNszRouLxs
GFr7v571WH+4x0Mtq9DCOVEe/22HjPkE4mivDDhxWELm8crLCPcc7v9eRVRB
davH+sM9HmpdhdaBcoIS/yVmXhztlUZ5HJaQeeTysuJ7Dvd/r0FUQfVqaErj
EQ+1rkLrADnBif8SMy+WJo3qOCwl88jlZdX3nDjc/00grKB6NDTlcY+HWleh
jQPiBCf+S8y8UJo8quOwhMxjl5cV33PicP83gThB69HQlMYrHuq7+Km/hQri
BCf+C2reExTzYmnyAMRhvSC187jlZeX3HAeorC2DAS1U3Qlaf/FQEdpbqD6g
ZV4aVeZ9S9N3frvuzoumkN78zuhvoepP0PqJh0qgu4UqDTnzsq9IlXmf0nSe
36668+IplDe/MwYUOcm0Vq1roRI0z/1fxOM7Fu48mSn+dj4pZhQ5ibVWHXta
qPTMizHDPM4U3vmuMCVVTClyEmutOva0UOmZF2GKeZwpvPNuUJqSEsYUOYm1
VhPY0UKlaN4TY8zjTOGdd4PSFLXQ6P/aGOJk87qgYYbNd4UpaqHR/7UxxMnm
dUHDDJvvClNUQ6P/a2OIk83rgoYZNt8VpjAMwzAMwzAMwzAMwzAMwzAMw6iC
i5y6YPO6YPO6YPOmwRVaXXCFVhfYFVo+g1/CdxvD0FqhBQ+V2lTk1FqhZfMu
5j2iur5ASNAKzqBF5rHuNnEgzq+F5pOiuUIL3f3UWeT0ieYKLZt3Me8e1fWH
+gSt6AxaZh7hbhMH4vwaYJ5IhRa2+4lS5CRSoWXzSc0L3og86hO0UmfQHvM4
zWuQ84to3gUiFVrg7idGkZNIhZbNJzfv/UbkUZ+glTqDFpnHaV5DnF9E8y6Q
qdCCdj+Bipy6W6g4FVoTzXuCYl7wRqTBSNDKnEF7dh6neQ1zfiHNB8aAIidO
i1M0C6rIqb2FalyFVjQFvYWqyry/N6I7QQuI9p33QQDtUOfXHPQXOXFanOJZ
YEVO3S1Uwyq04inYLVRl5v28Ef0JWkh077w0gbRDnV9jMKDIidPiRJjFLVRd
U2zs/xLQ7li482h3G8zbWoqYUeTErGTizOIWqq4pYowxT0y7LTuPJsSUhXfF
lCInZiUTZxa3UHVNEWGQeWLabdl5NCFmLLwbxhQ5MSuZWLO4hapnigCTzJPT
bsfOowkxYuGDQ6lSaleRk1KllM3jj0CbAgiZu4115pNDqVJqV5GTUqWUzeOP
QJsCCJm7jXXm3aBUKbWryEmpUsrm8UegTQGEzN3GOvMMwzAMGf4PdgZ59A==

    "], {{0, 78}, {512, 0}}, {0, 255},
    ColorFunction->RGBColor],
   BoxForm`ImageTag["Byte", ColorSpace -> "RGB", Interleaving -> True],
   Selectable->False],
  DefaultBaseStyle->"ImageGraphics",
  ImageSize->Automatic,
  ImageSizeRaw->{512, 78},
  PlotRange->{{0, 512}, {0, 78}}]], "Output",
 ImageSize->{516, 78},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"RasterizedOutput",
 CellLabel->"Out[2]=",
 CellID->410432361]
}, Open  ]],

Cell[BoxData[
 RowBox[{
  RowBox[{"FCSetDiracGammaScheme", "[", "\"\<NDR\>\"", "]"}], ";"}]], "Input",\

 CellLabel->"In[3]:="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 InterpretationBox[Cell["\t", "ExampleDelimiter"],
  $Line = 0; Null]], "ExampleDelimiter"],

Cell[TextData[{
 "Sorting of the matrices inside ",
 Cell[BoxData["4"], "InlineFormula"],
 "-dimensional traces helps to avoid some spurious terms."
}], "Notes"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"DiracTrace", "[", 
    RowBox[{
     RowBox[{"GA", "[", 
      RowBox[{
      "\[Mu]", ",", "\[Nu]", ",", "5", ",", "\[Rho]", ",", "\[Sigma]", ",", 
       "\[Tau]", ",", "\[Kappa]"}], "]"}], ",", 
     RowBox[{"DiracTraceEvaluate", "\[Rule]", "True"}]}], "]"}], "-", 
   RowBox[{"DiracTrace", "[", 
    RowBox[{
     RowBox[{"GA", "[", 
      RowBox[{
      "\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Sigma]", ",", "\[Tau]", 
       ",", "\[Kappa]", ",", "5"}], "]"}], ",", 
     RowBox[{"DiracTraceEvaluate", "\[Rule]", "True"}]}], "]"}]}], "//", 
  "Expand"}]], "Input",
 CellLabel->"In[1]:="],

Cell[BoxData[
 FormBox["0", TraditionalForm]], "Output",
 ImageSize->{13, 14},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[1]="]
}, Open  ]],

Cell[TextData[{
 "When the sorting is turned off via ",
 Cell[BoxData[
  RowBox[{"Sort", "\[Rule]", "True"}]], "InlineFormula"],
 ", one may obtain some spurious terms that vanish by Schouten's identity."
}], "Notes"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{
   RowBox[{"DiracTrace", "[", 
    RowBox[{
     RowBox[{"GA", "[", 
      RowBox[{
      "\[Mu]", ",", "\[Nu]", ",", "5", ",", "\[Rho]", ",", "\[Sigma]", ",", 
       "\[Tau]", ",", "\[Kappa]"}], "]"}], ",", 
     RowBox[{"DiracTraceEvaluate", "\[Rule]", "True"}], ",", 
     RowBox[{"Sort", "\[Rule]", "False"}]}], "]"}], "-", 
   RowBox[{"DiracTrace", "[", 
    RowBox[{
     RowBox[{"GA", "[", 
      RowBox[{
      "\[Mu]", ",", "\[Nu]", ",", "\[Rho]", ",", "\[Sigma]", ",", "\[Tau]", 
       ",", "\[Kappa]", ",", "5"}], "]"}], ",", 
     RowBox[{"DiracTraceEvaluate", "\[Rule]", "True"}], ",", 
     RowBox[{"Sort", "\[Rule]", "False"}]}], "]"}]}], "//", 
  "Expand"}]], "Input",
 CellLabel->"In[2]:="],

Cell[BoxData[
 GraphicsBox[
  TagBox[RasterBox[CompressedData["
1:eJztnQtQTWkAgLNrdnfs7CxrDLOmGaxHISmzKUQpWU07VHYLsTQlQkxFtp0t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    "], {{0, 35}, {481, 
    0}}, {0, 255},
    ColorFunction->RGBColor],
   BoxForm`ImageTag["Byte", ColorSpace -> "RGB", Interleaving -> True],
   Selectable->False],
  DefaultBaseStyle->"ImageGraphics",
  ImageSize->Automatic,
  ImageSizeRaw->{481, 35},
  PlotRange->{{0, 481}, {0, 35}}]], "Output",
 ImageSize->{485, 35},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"RasterizedOutput",
 CellLabel->"Out[2]=",
 CellID->694955970]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 InterpretationBox[Cell["\t", "ExampleDelimiter"],
  $Line = 0; Null]], "ExampleDelimiter"],

Cell["\<\
The trace of the unit matrix in the Dirac space is fixed to 4, which is the \
standard choice in dimensional regularization.\
\>", "Notes"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DiracTrace", "[", "1", "]"}]], "Input",
 CellLabel->"In[1]:="],

Cell[BoxData[
 FormBox[
  RowBox[{"tr", "(", 
   FormBox["1",
    TraditionalForm], ")"}], TraditionalForm]], "Output",
 ImageSize->{34, 16},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[1]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DiracSimplify", "[", "%", "]"}]], "Input",
 CellLabel->"In[2]:="],

Cell[BoxData[
 FormBox["4", TraditionalForm]], "Output",
 ImageSize->{13, 14},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[2]="]
}, Open  ]],

Cell[TextData[{
 "If, for some reason, this value must be modified, one can do so using the \
option ",
 ButtonBox["TraceOfOne",
  BaseStyle->"Link",
  ButtonData->"paclet:FeynCalc/ref/TraceOfOne",
  ButtonNote->"TraceOfOne"],
 "."
}], "Notes"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DiracTrace", "[", 
  RowBox[{"1", ",", 
   RowBox[{"TraceOfOne", "\[Rule]", "D"}], ",", 
   RowBox[{"DiracTraceEvaluate", "\[Rule]", "True"}]}], "]"}]], "Input",
 CellLabel->"In[3]:="],

Cell[BoxData[
 FormBox["D", TraditionalForm]], "Output",
 ImageSize->{19, 14},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[3]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DiracSimplify", "[", 
  RowBox[{"DiracTrace", "[", 
   RowBox[{
    RowBox[{"GAD", "[", 
     RowBox[{"\[Mu]", ",", "\[Nu]"}], "]"}], ",", 
    RowBox[{"TraceOfOne", "\[Rule]", "D"}]}], "]"}], "]"}]], "Input",
 CellLabel->"In[4]:="],

Cell[BoxData[
 FormBox[
  RowBox[{"D", " ", 
   SuperscriptBox["g", 
    RowBox[{
     FormBox[
      FormBox["\[Mu]",
       TraditionalForm],
      TraditionalForm], 
     FormBox[
      FormBox["\[Nu]",
       TraditionalForm],
      TraditionalForm]}]]}], TraditionalForm]], "Output",
 ImageSize->{53, 16},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[4]="]
}, Open  ]]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 InterpretationBox[Cell["\t", "ExampleDelimiter"],
  $Line = 0; Null]], "ExampleDelimiter"],

Cell["\<\
Since FeynCalc 9.3 it is also possible to compute traces of Dirac matrices \
with Cartesian or temporal indices. However, the support of nonrelativistic \
calculations is a very new feature, so that things may not work as smooth as \
they do for manifestly Lorentz covariant expressions.\
\>", "Notes"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DiracTrace", "[", 
  RowBox[{"CGAD", "[", 
   RowBox[{"i", ",", "j", ",", "k", ",", "l"}], "]"}], "]"}]], "Input",
 CellLabel->"In[1]:="],

Cell[BoxData[
 FormBox[
  RowBox[{"tr", "(", 
   FormBox[
    RowBox[{
     FormBox[
      SuperscriptBox[
       FormBox[
        StyleBox["\<\"\[Gamma]\"\>",
         StripOnInput->False,
         FontWeight->Bold],
        TraditionalForm], 
       FormBox[
        FormBox[
         StyleBox["i",
          StripOnInput->False,
          FontWeight->Bold],
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       FormBox[
        StyleBox["\<\"\[Gamma]\"\>",
         StripOnInput->False,
         FontWeight->Bold],
        TraditionalForm], 
       FormBox[
        FormBox[
         StyleBox["j",
          StripOnInput->False,
          FontWeight->Bold],
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       FormBox[
        StyleBox["\<\"\[Gamma]\"\>",
         StripOnInput->False,
         FontWeight->Bold],
        TraditionalForm], 
       FormBox[
        FormBox[
         StyleBox["k",
          StripOnInput->False,
          FontWeight->Bold],
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       FormBox[
        StyleBox["\<\"\[Gamma]\"\>",
         StripOnInput->False,
         FontWeight->Bold],
        TraditionalForm], 
       FormBox[
        FormBox[
         StyleBox["l",
          StripOnInput->False,
          FontWeight->Bold],
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm]}],
    TraditionalForm], ")"}], TraditionalForm]], "Output",
 ImageSize->{123, 25},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[1]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DiracSimplify", "[", "%", "]"}]], "Input",
 CellLabel->"In[2]:="],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"4", " ", 
    SuperscriptBox["\[Delta]", 
     RowBox[{
      FormBox[
       FormBox[
        StyleBox["i",
         StripOnInput->False,
         FontWeight->Bold],
        TraditionalForm],
       TraditionalForm], 
      FormBox[
       FormBox[
        StyleBox["l",
         StripOnInput->False,
         FontWeight->Bold],
        TraditionalForm],
       TraditionalForm]}]], " ", 
    SuperscriptBox["\[Delta]", 
     RowBox[{
      FormBox[
       FormBox[
        StyleBox["j",
         StripOnInput->False,
         FontWeight->Bold],
        TraditionalForm],
       TraditionalForm], 
      FormBox[
       FormBox[
        StyleBox["k",
         StripOnInput->False,
         FontWeight->Bold],
        TraditionalForm],
       TraditionalForm]}]]}], "-", 
   RowBox[{"4", " ", 
    SuperscriptBox["\[Delta]", 
     RowBox[{
      FormBox[
       FormBox[
        StyleBox["i",
         StripOnInput->False,
         FontWeight->Bold],
        TraditionalForm],
       TraditionalForm], 
      FormBox[
       FormBox[
        StyleBox["k",
         StripOnInput->False,
         FontWeight->Bold],
        TraditionalForm],
       TraditionalForm]}]], " ", 
    SuperscriptBox["\[Delta]", 
     RowBox[{
      FormBox[
       FormBox[
        StyleBox["j",
         StripOnInput->False,
         FontWeight->Bold],
        TraditionalForm],
       TraditionalForm], 
      FormBox[
       FormBox[
        StyleBox["l",
         StripOnInput->False,
         FontWeight->Bold],
        TraditionalForm],
       TraditionalForm]}]]}], "+", 
   RowBox[{"4", " ", 
    SuperscriptBox["\[Delta]", 
     RowBox[{
      FormBox[
       FormBox[
        StyleBox["i",
         StripOnInput->False,
         FontWeight->Bold],
        TraditionalForm],
       TraditionalForm], 
      FormBox[
       FormBox[
        StyleBox["j",
         StripOnInput->False,
         FontWeight->Bold],
        TraditionalForm],
       TraditionalForm]}]], " ", 
    SuperscriptBox["\[Delta]", 
     RowBox[{
      FormBox[
       FormBox[
        StyleBox["k",
         StripOnInput->False,
         FontWeight->Bold],
        TraditionalForm],
       TraditionalForm], 
      FormBox[
       FormBox[
        StyleBox["l",
         StripOnInput->False,
         FontWeight->Bold],
        TraditionalForm],
       TraditionalForm]}]]}]}], TraditionalForm]], "Output",
 ImageSize->{261, 18},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[2]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DiracTrace", "[", 
  RowBox[{
   RowBox[{"CGA", "[", 
    RowBox[{"i", ",", "j", ",", "k", ",", "l"}], "]"}], ".", 
   RowBox[{"GA", "[", "6", "]"}], ".", 
   RowBox[{"CGA", "[", 
    RowBox[{"m", ",", "n"}], "]"}]}], "]"}]], "Input",
 CellLabel->"In[3]:="],

Cell[BoxData[
 FormBox[
  RowBox[{"tr", "(", 
   FormBox[
    RowBox[{
     FormBox[
      SuperscriptBox[
       OverscriptBox[
        FormBox[
         StyleBox["\<\"\[Gamma]\"\>",
          StripOnInput->False,
          FontWeight->Bold],
         TraditionalForm], "_"], 
       FormBox[
        FormBox[
         StyleBox["i",
          StripOnInput->False,
          FontWeight->Bold],
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox[
        FormBox[
         StyleBox["\<\"\[Gamma]\"\>",
          StripOnInput->False,
          FontWeight->Bold],
         TraditionalForm], "_"], 
       FormBox[
        FormBox[
         StyleBox["j",
          StripOnInput->False,
          FontWeight->Bold],
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox[
        FormBox[
         StyleBox["\<\"\[Gamma]\"\>",
          StripOnInput->False,
          FontWeight->Bold],
         TraditionalForm], "_"], 
       FormBox[
        FormBox[
         StyleBox["k",
          StripOnInput->False,
          FontWeight->Bold],
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox[
        FormBox[
         StyleBox["\<\"\[Gamma]\"\>",
          StripOnInput->False,
          FontWeight->Bold],
         TraditionalForm], "_"], 
       FormBox[
        FormBox[
         StyleBox["l",
          StripOnInput->False,
          FontWeight->Bold],
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox["\[Gamma]", "_"], 
       FormBox["6",
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox[
        FormBox[
         StyleBox["\<\"\[Gamma]\"\>",
          StripOnInput->False,
          FontWeight->Bold],
         TraditionalForm], "_"], 
       FormBox[
        FormBox[
         StyleBox["m",
          StripOnInput->False,
          FontWeight->Bold],
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], ".", 
     FormBox[
      SuperscriptBox[
       OverscriptBox[
        FormBox[
         StyleBox["\<\"\[Gamma]\"\>",
          StripOnInput->False,
          FontWeight->Bold],
         TraditionalForm], "_"], 
       FormBox[
        FormBox[
         StyleBox["n",
          StripOnInput->False,
          FontWeight->Bold],
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm]}],
    TraditionalForm], ")"}], TraditionalForm]], "Output",
 ImageSize->{203, 25},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[3]="]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"DiracSimplify", "[", "%", "]"}]], "Input",
 CellLabel->"In[4]:="],

Cell[BoxData[
 GraphicsBox[
  TagBox[RasterBox[CompressedData["
1:eJztnQ1QFPX/xzWnQ/SakD1E4Uh5DBk9Ek08pSwIFVOxVMCppqSgfIRCIx1n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    "], {{0, 85}, {540, 0}}, {0, 255},
    ColorFunction->RGBColor],
   BoxForm`ImageTag["Byte", ColorSpace -> "RGB", Interleaving -> True],
   Selectable->False],
  DefaultBaseStyle->"ImageGraphics",
  ImageSize->Automatic,
  ImageSizeRaw->{540, 85},
  PlotRange->{{0, 540}, {0, 85}}]], "Output",
 ImageSize->{544, 85},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"RasterizedOutput",
 CellLabel->"Out[4]=",
 CellID->1583542038]
}, Open  ]]
}, Open  ]]
}, Open  ]],

Cell["", "SectionFooterSpacer"]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 Cell[BoxData[
  InterpretationBox[
   StyleBox[
    GraphicsBox[{},
     BaselinePosition->Baseline,
     ImageSize->{6, 0}],
    CacheGraphics->False],
   Spacer[6]]]],
 "See Also"
}], "SeeAlsoSection",
 WholeCellGroupOpener->True,
 CellID->1255426704],

Cell[TextData[{
 StyleBox[ButtonBox["Contract",
  BaseStyle->"Link",
  ButtonData->"paclet:FeynCalc/ref/Contract",
  ButtonNote->"Contract"],
  FontFamily->"Verdana"],
 ", ",
 StyleBox[ButtonBox["DiracEquation",
  BaseStyle->"Link",
  ButtonData->"paclet:FeynCalc/ref/DiracEquation",
  ButtonNote->"DiracEquation"],
  FontFamily->"Verdana"],
 ", ",
 StyleBox[ButtonBox["DiracGamma",
  BaseStyle->"Link",
  ButtonData->"paclet:FeynCalc/ref/DiracGamma",
  ButtonNote->"DiracGamma"],
  FontFamily->"Verdana"],
 ", ",
 StyleBox[ButtonBox["DiracGammaExpand",
  BaseStyle->"Link",
  ButtonData->"paclet:FeynCalc/ref/DiracGammaCombine",
  ButtonNote->"DiracGammaCombine"],
  FontFamily->"Verdana"],
 ", ",
 StyleBox[ButtonBox["DiracTrick",
  BaseStyle->"Link",
  ButtonData->"paclet:FeynCalc/ref/DiracTrick",
  ButtonNote->"DiracTrick"],
  FontFamily->"Verdana"],
 ", ",
 StyleBox[ButtonBox["FCGetDiracGammaScheme",
  BaseStyle->"Link",
  ButtonData->"paclet:FeynCalc/ref/FCSetDiracGammaScheme",
  ButtonNote->"FCSetDiracGammaScheme"],
  FontFamily->"Verdana"],
 ", ",
 StyleBox[ButtonBox["FCSetDiracGammaScheme",
  BaseStyle->"Link",
  ButtonData->"paclet:FeynCalc/ref/FCGetDiracGammaScheme",
  ButtonNote->"FCSetDiracGammaScheme"],
  FontFamily->"Verdana"],
 "."
}], "SeeAlso"]
}, Open  ]],

Cell[" ", "FooterCell"]
},
Saveable->False,
ScreenStyleEnvironment->"Working",
WindowSize->{725, 750},
WindowMargins->{{-10, Automatic}, {Automatic, -8}},
WindowTitle->"DiracTrace",
TaggingRules->{
 "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> 
  GridBox[{{
      RowBox[{
        ButtonBox[
        "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", 
         BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> 
    Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> 
  None, "RootCaptions" -> "", 
  "Metadata" -> {
   "built" -> "{2020, 6, 20, 19, 4, 14.612367}", 
    "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", 
    "keywords" -> {}, "specialkeywords" -> {}, 
    "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> 
    "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> 
    "None", "summary" -> 
    "DiracTrace[exp] is the head of Dirac traces. By default the trace is not \
evaluated. The evaluation occurs only when the option DiracTraceEvaluate is \
set to True. It is recommended to use DiracSimplify, which will automatically \
evaluate all Dirac traces in the input expression.", "synonyms" -> {}, 
    "tabletags" -> {}, "title" -> "DiracTrace", "titlemodifier" -> "", 
    "windowtitle" -> "DiracTrace", "type" -> "Symbol", "uri" -> 
    "FeynCalc/ref/DiracTrace"}, "SearchTextTranslated" -> ""},
CellContext->"Global`",
FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)",
StyleDefinitions->Notebook[{
   Cell[
    StyleData[
    StyleDefinitions -> FrontEnd`FileName[{"Wolfram"}, "Reference.nb"]]], 
   Cell[
    StyleData["Input"], CellContext -> "Global`"], 
   Cell[
    StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, 
  FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", 
  StyleDefinitions -> "Default.nb"]
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{
 "PrimaryExamplesSection"->{
  Cell[7444, 217, 389, 15, 31, "PrimaryExamplesSection",
   CellTags->"PrimaryExamplesSection",
   CellID->1070442148]},
 "DiracTrace"->{
  Cell[8148, 248, 191, 6, 27, "Input",
   CellTags->"DiracTrace",
   CellID->60676203],
  Cell[8342, 256, 661, 26, 40, "Output",
   CellTags->"DiracTrace"],
  Cell[9040, 287, 228, 7, 27, "Input",
   CellTags->"DiracTrace",
   CellID->1088537337],
  Cell[9271, 296, 1068, 42, 40, "Output",
   CellTags->"DiracTrace"],
  Cell[10789, 359, 303, 9, 27, "Input",
   CellTags->"DiracTrace",
   CellID->710007181],
  Cell[11095, 370, 1966, 78, 40, "Output",
   CellTags->"DiracTrace"],
  Cell[20145, 743, 238, 7, 27, "Input",
   CellTags->"DiracTrace",
   CellID->196468068],
  Cell[20386, 752, 1221, 48, 43, "Output",
   CellTags->"DiracTrace"]},
 "RasterizedOutput"->{
  Cell[24388, 920, 3218, 61, 59, "Output",
   CellTags->"RasterizedOutput",
   CellID->745659537],
  Cell[29607, 1066, 6447, 114, 133, "Output",
   CellTags->"RasterizedOutput",
   CellID->837611303],
  Cell[43892, 1501, 4588, 83, 98, "Output",
   CellTags->"RasterizedOutput",
   CellID->249793213],
  Cell[50589, 1672, 7455, 130, 139, "Output",
   CellTags->"RasterizedOutput",
   CellID->715016264],
  Cell[58936, 1834, 22681, 380, 472, "Output",
   CellTags->"RasterizedOutput",
   CellID->253055425],
  Cell[95748, 2737, 4674, 85, 98, "Output",
   CellTags->"RasterizedOutput",
   CellID->410432361],
  Cell[102714, 2905, 3385, 64, 56, "Output",
   CellTags->"RasterizedOutput",
   CellID->694955970],
  Cell[116718, 3412, 9327, 161, 101, "Output",
   CellTags->"RasterizedOutput",
   CellID->1583542038]}
 }
*)
(*CellTagsIndex
CellTagsIndex->{
 {"PrimaryExamplesSection", 129750, 3691},
 {"DiracTrace", 129888, 3695},
 {"RasterizedOutput", 130551, 3716}
 }
*)
(*NotebookFileOutline
Notebook[{
Cell[582, 21, 3655, 86, 53, "AnchorBarGrid",
 CellID->1],
Cell[4240, 109, 287, 11, 45, "ObjectNameGrid"],
Cell[CellGroupData[{
Cell[4552, 124, 951, 25, 119, "Usage",
 CellID->982511436],
Cell[CellGroupData[{
Cell[5528, 153, 738, 24, 31, "NotesSection",
 CellGroupingRules->{"SectionGrouping", 50},
 CellID->894721589],
Cell[6269, 179, 31, 0, 14, "SectionHeaderSpacer"],
Cell[CellGroupData[{
Cell[6325, 183, 93, 2, 27, "Input"],
Cell[6421, 187, 962, 23, 94, "Output"]
}, Open  ]]
}, Closed]]
}, Open  ]],
Cell[CellGroupData[{
Cell[7444, 217, 389, 15, 31, "PrimaryExamplesSection",
 CellTags->"PrimaryExamplesSection",
 CellID->1070442148],
Cell[CellGroupData[{
Cell[7858, 236, 197, 6, 26, "ExampleSection",
 CellID->1068112497],
Cell[8058, 244, 65, 0, 32, "Notes"],
Cell[CellGroupData[{
Cell[8148, 248, 191, 6, 27, "Input",
 CellTags->"DiracTrace",
 CellID->60676203],
Cell[8342, 256, 661, 26, 40, "Output",
 CellTags->"DiracTrace"]
}, Open  ]],
Cell[CellGroupData[{
Cell[9040, 287, 228, 7, 27, "Input",
 CellTags->"DiracTrace",
 CellID->1088537337],
Cell[9271, 296, 1068, 42, 40, "Output",
 CellTags->"DiracTrace"]
}, Open  ]],
Cell[10354, 341, 410, 14, 32, "Notes"],
Cell[CellGroupData[{
Cell[10789, 359, 303, 9, 27, "Input",
 CellTags->"DiracTrace",
 CellID->710007181],
Cell[11095, 370, 1966, 78, 40, "Output",
 CellTags->"DiracTrace"]
}, Open  ]],
Cell[CellGroupData[{
Cell[13098, 453, 225, 6, 27, "Input"],
Cell[13326, 461, 1784, 75, 37, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[15147, 541, 159, 4, 27, "Input"],
Cell[15309, 547, 1327, 49, 37, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[16673, 601, 89, 2, 27, "Input"],
Cell[16765, 605, 2306, 93, 37, "Output"]
}, Open  ]],
Cell[19086, 701, 678, 23, 66, "Notes"],
Cell[CellGroupData[{
Cell[19789, 728, 105, 2, 9, "ExampleDelimiter"],
Cell[19897, 732, 223, 7, 32, "Notes"],
Cell[CellGroupData[{
Cell[20145, 743, 238, 7, 27, "Input",
 CellTags->"DiracTrace",
 CellID->196468068],
Cell[20386, 752, 1221, 48, 43, "Output",
 CellTags->"DiracTrace"]
}, Open  ]],
Cell[CellGroupData[{
Cell[21644, 805, 89, 2, 27, "Input"],
Cell[21736, 809, 651, 26, 35, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[22424, 840, 230, 6, 27, "Input"],
Cell[22657, 848, 1602, 63, 43, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[24296, 916, 89, 2, 27, "Input"],
Cell[24388, 920, 3218, 61, 59, "Output",
 CellTags->"RasterizedOutput",
 CellID->745659537]
}, Open  ]],
Cell[CellGroupData[{
Cell[27643, 986, 230, 6, 27, "Input"],
Cell[27876, 994, 1602, 63, 42, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[29515, 1062, 89, 2, 27, "Input"],
Cell[29607, 1066, 6447, 114, 133, "Output",
 CellTags->"RasterizedOutput",
 CellID->837611303]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[36103, 1186, 105, 2, 9, "ExampleDelimiter"],
Cell[36211, 1190, 201, 6, 32, "Notes"],
Cell[CellGroupData[{
Cell[36437, 1200, 529, 16, 46, "Input"],
Cell[36969, 1218, 1273, 48, 40, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[38279, 1271, 89, 2, 27, "Input"],
Cell[38371, 1275, 2619, 114, 40, "Output"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[41039, 1395, 105, 2, 9, "ExampleDelimiter"],
Cell[41147, 1399, 648, 15, 83, "Notes"],
Cell[CellGroupData[{
Cell[41820, 1418, 353, 9, 27, "Input"],
Cell[42176, 1429, 1587, 63, 43, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[43800, 1497, 89, 2, 27, "Input"],
Cell[43892, 1501, 4588, 83, 98, "Output",
 CellTags->"RasterizedOutput",
 CellID->249793213]
}, Open  ]],
Cell[CellGroupData[{
Cell[48517, 1589, 353, 9, 27, "Input"],
Cell[48873, 1600, 1587, 63, 43, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[50497, 1668, 89, 2, 27, "Input"],
Cell[50589, 1672, 7455, 130, 139, "Output",
 CellTags->"RasterizedOutput",
 CellID->715016264]
}, Open  ]],
Cell[58059, 1805, 318, 7, 66, "Notes"],
Cell[58380, 1814, 128, 4, 27, "Input"],
Cell[CellGroupData[{
Cell[58533, 1822, 400, 10, 27, "Input"],
Cell[58936, 1834, 22681, 380, 472, "Output",
 CellTags->"RasterizedOutput",
 CellID->253055425]
}, Open  ]],
Cell[81632, 2217, 908, 20, 117, "Notes"]
}, Open  ]],
Cell[CellGroupData[{
Cell[82577, 2242, 105, 2, 9, "ExampleDelimiter"],
Cell[82685, 2246, 448, 11, 66, "Notes"],
Cell[83136, 2259, 127, 4, 27, "Input"],
Cell[CellGroupData[{
Cell[83288, 2267, 542, 16, 46, "Input"],
Cell[83833, 2285, 1439, 54, 40, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[85309, 2344, 89, 2, 27, "Input"],
Cell[85401, 2348, 1005, 17, 193, "Message"],
Cell[86409, 2367, 173, 5, 35, "Output"]
}, Open  ]],
Cell[86597, 2375, 128, 4, 27, "Input"],
Cell[CellGroupData[{
Cell[86750, 2383, 569, 16, 46, "Input"],
Cell[87322, 2401, 2931, 125, 40, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[90290, 2531, 110, 3, 27, "Input"],
Cell[90403, 2536, 1153, 36, 70, "Output"]
}, Open  ]],
Cell[91571, 2575, 127, 4, 27, "Input"],
Cell[91701, 2581, 190, 6, 32, "Notes"]
}, Open  ]],
Cell[CellGroupData[{
Cell[91928, 2592, 105, 2, 9, "ExampleDelimiter"],
Cell[92036, 2596, 448, 13, 49, "Notes"],
Cell[92487, 2611, 128, 4, 27, "Input"],
Cell[CellGroupData[{
Cell[92640, 2619, 512, 14, 45, "Input"],
Cell[93155, 2635, 225, 7, 37, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[93417, 2647, 588, 16, 45, "Input"],
Cell[94008, 2665, 224, 7, 37, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[94269, 2677, 76, 2, 27, "Input"],
Cell[94348, 2681, 169, 5, 35, "Output"]
}, Open  ]],
Cell[94532, 2689, 127, 4, 27, "Input"],
Cell[94662, 2695, 109, 3, 27, "Input"]
}, Open  ]],
Cell[CellGroupData[{
Cell[94808, 2703, 105, 2, 9, "ExampleDelimiter"],
Cell[94916, 2707, 265, 8, 53, "ExampleText",
 CellID->2003592022],
Cell[95184, 2717, 136, 4, 27, "Input"],
Cell[CellGroupData[{
Cell[95345, 2725, 400, 10, 27, "Input"],
Cell[95748, 2737, 4674, 85, 98, "Output",
 CellTags->"RasterizedOutput",
 CellID->410432361]
}, Open  ]],
Cell[100437, 2825, 127, 4, 27, "Input"]
}, Open  ]],
Cell[CellGroupData[{
Cell[100601, 2834, 105, 2, 9, "ExampleDelimiter"],
Cell[100709, 2838, 161, 4, 32, "Notes"],
Cell[CellGroupData[{
Cell[100895, 2846, 646, 18, 62, "Input"],
Cell[101544, 2866, 166, 5, 35, "Output"]
}, Open  ]],
Cell[101725, 2874, 217, 5, 49, "Notes"],
Cell[CellGroupData[{
Cell[101967, 2883, 744, 20, 62, "Input"],
Cell[102714, 2905, 3385, 64, 56, "Output",
 CellTags->"RasterizedOutput",
 CellID->694955970]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[106148, 2975, 105, 2, 9, "ExampleDelimiter"],
Cell[106256, 2979, 149, 3, 49, "Notes"],
Cell[CellGroupData[{
Cell[106430, 2986, 86, 2, 27, "Input"],
Cell[106519, 2990, 229, 8, 37, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[106785, 3003, 89, 2, 27, "Input"],
Cell[106877, 3007, 166, 5, 35, "Output"]
}, Open  ]],
Cell[107058, 3015, 244, 8, 32, "Notes"],
Cell[CellGroupData[{
Cell[107327, 3027, 208, 5, 27, "Input"],
Cell[107538, 3034, 166, 5, 35, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[107741, 3044, 256, 7, 27, "Input"],
Cell[108000, 3053, 398, 16, 37, "Output"]
}, Open  ]]
}, Open  ]],
Cell[CellGroupData[{
Cell[108447, 3075, 105, 2, 9, "ExampleDelimiter"],
Cell[108555, 3079, 312, 5, 66, "Notes"],
Cell[CellGroupData[{
Cell[108892, 3088, 161, 4, 27, "Input"],
Cell[109056, 3094, 1731, 69, 46, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[110824, 3168, 89, 2, 27, "Input"],
Cell[110916, 3172, 2522, 105, 39, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[113475, 3282, 281, 8, 27, "Input"],
Cell[113759, 3292, 2830, 111, 46, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[116626, 3408, 89, 2, 27, "Input"],
Cell[116718, 3412, 9327, 161, 101, "Output",
 CellTags->"RasterizedOutput",
 CellID->1583542038]
}, Open  ]]
}, Open  ]]
}, Open  ]],
Cell[126084, 3578, 31, 0, 29, "SectionFooterSpacer"]
}, Open  ]],
Cell[CellGroupData[{
Cell[126152, 3583, 270, 12, 31, "SeeAlsoSection",
 CellID->1255426704],
Cell[126425, 3597, 1272, 43, 71, "SeeAlso"]
}, Open  ]],
Cell[127712, 3643, 23, 0, 41, "FooterCell"]
}
]
*)

(* End of internal cache information *)

